Cluster analysis and continuum percolation of 3D square-well phases MC and PY solutions

Abstract

An extensive study of the percolation threshold, ρ_p of three dimensional attractive and repulsive square well fluids is made by Monte Carlo computer simulation. We find that in the hard-core limit an attractive well decreases ρ_p below the high temperature limiting value. In contrast a hard shoulder potential produces the opposite trend. A numerical solution of the PY integral equations employing Hill's concept of bound and unbound pairs gives results qualitatively in agreement with MC. The PY solution overestimates ρ_p especially in the hard-core limit and at high temperature. We examine the shapes of all the clusters at the percolation threshold, resolved as a function of the number of particles in a cluster, s. The asphericity parameter, A ₃, describing the instantaneous shape of the cluster decays slowly from unity, typically only achieving ∼ 0·3 by s ∼ 100, close to the estimated universal value of 0·312.